Classification of out-of-time-order correlators

Haehl, Felix M., Loganayagam, R., Narayan, Prithvi and Rangamani, Mukund (2019) Classification of out-of-time-order correlators. SciPost Phys., 6 (001), [001]. (doi:10.21468/SciPostPhys.6.1.001).

Record type: Article

Abstract

The space of n-point correlation functions, for all possible time-orderings of operators, can be computed by a non-trivial path integral contour, which depends on how many time-ordering violations are present in the correlator. These contours, which have come to be known as timefolds, or out-of-time-order (OTO) contours, are a natural generalization of the Schwinger-Keldysh contour (which computes singly out-of-time-ordered correlation functions). We provide a detailed discussion of such higher OTO functional integrals, explaining their general structure, and the myriad ways in which a particular correlation function may be encoded in such contours. Our discussion may be seen as a natural generalization of the Schwinger-Keldysh formalism to higher OTO correlation functions. We provide explicit illustration for low point correlators (n=2,3,4) to exemplify the general statements.

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1701.02820v4 - Accepted Manuscript

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Submitted date: 11 January 2017

Accepted/In Press date: 19 December 2018

Published date: 7 January 2019

Additional Information: Funded by Simons Foundation 48 pages + appendices. v2: added references and minor clarifications. v3: additional clarifications and examples added. v4: presentational improvements

Keywords: hep-th, cond-mat.stat-mech, quant-ph